RICHARD HOSHINO National Institute of Informatics, Tokyo Visit to ASIJ September 14 th , 2012

1. RICHARD HOSHINONational Institute of Informatics, TokyoVisit to ASIJSeptember 14th, 2012 Three Problem-Solving StrategiesFor Mathematics and For Life

2. Activity #1 Fill in the Blanks 24 H____ in a D__= 24 Hours in a Day

3. Problem-Solving Strategy #1 Start with what you know to uncover what you don’t know “True learning involves figuring out how to use what you already know in order to go beyond what you already think.” – Jerome Bruner

4. Sudoku and Crossword Puzzles

5. Canada Border Services Agency

6. Marine Container Shipping

7. Improving Risk-Assessment

8. Activity #2 Triangle Magic

9. Problem-Solving Strategy #2 Challenge all of your assumptions “Begin challenging your own assumptions. Your assumptions are your windows on the world. Scrub them off every once in awhile, or the light won't come in.” – Alan Alda

10. Euclid’s Five Axioms • Can draw a straight line from any point to any point. • Can extend a finite straight line continuously. • Can describe a circle with any centre and radius. • All right angles are equal to one another. • Two non-parallel lines have a point of intersection.

11. Activity #3 Game of Fifteen

12. Problem-Solving Strategy #3 Convert difficult problems into equivalent simpler problems “To raise new questions, new possibilities,to regard old problems from a new angle, requires creative imagination and marks real advance in science.”– Albert Einstein

13. Environmental Sustainability • What is the optimal way to design a cylindrical can to minimize manufacturing waste?

14. Schedules for Pro Baseball

15. Graph Theory

16. Tokyo Subway System

17. Key Insight These two problems are equivalent! =

18. Recap of Three Main Points • Start with what you know to uncover what you don’t know. • Challenge all of your assumptions. • Convert difficult problems into equivalent simpler problems.